show that points A(1,3) b(2,6) c(5,7) and d(4, 4) are vertex of a rhombus.
Answers
Answer:
ABCD is a rhombus!
Step-by-step explanation:
Given points are A(1,3), B(2,6), C(5,7) and D(4,4).
∴ Distance between two points(x₁,y₁) and (x₂,y₂) = √(x₂ - x₁)² + (y₂ - y₁)².
(i) Distance between the points A and B:
AB = √(2 - 1)² + (6 - 3)²
= √1² + 3²
= √10 units
(ii) Distance between the points B and C:
BC = √(5 - 2)² + (7 - 6)²
= √3² + 1²
= √10 units
(iii) Distance between the points C and D:
CD = √(4 - 5)² + (4 - 7)²
= √(-1)² + (-3)²
= √10 units
(iv) Distance between the points D and A:
DA = √(4 - 1)² + (4 - 3)²
= √(3)² + (1)²
= √10 units.
Lengths of opposite sides are equal. We need to find the diagonals AC and BD.
Distance between the points A and C:
= √(5 - 1)² + (7 - 3)²
= √4² + 4²
= √32 units.
Distance between the points B and D:
= √(4 - 2)² + (4 - 6)²
= √2² + (-2)²
= √4 + 4
= √16
= 4 units
∴ ABCD is a quadrilateral whose sides are equal but diagonals are not equal. Thus ABCD is a rhombus.
Hope it helps!
ABCD is a rhombus!
Step-by-step explanation:
Given points are A(1,3), B(2,6), C(5,7) and D(4,4).
∴ Distance between two points(x₁,y₁) and (x₂,y₂) = √(x₂ - x₁)² + (y₂ - y₁)².
(i) Distance between the points A and B:
AB = √(2 - 1)² + (6 - 3)²
= √1² + 3²
= √10 units
(ii) Distance between the points B and C:
BC = √(5 - 2)² + (7 - 6)²
= √3² + 1²
= √10 units
(iii) Distance between the points C and D:
CD = √(4 - 5)² + (4 - 7)²
= √(-1)² + (-3)²
= √10 units
(iv) Distance between the points D and A:
DA = √(4 - 1)² + (4 - 3)²
= √(3)² + (1)²
= √10 units.
Lengths of opposite sides are equal. We need to find the diagonals AC and BD.
Distance between the points A and C:
= √(5 - 1)² + (7 - 3)²
= √4² + 4²
= √32 units.
Distance between the points B and D:
= √(4 - 2)² + (4 - 6)²
= √2² + (-2)²
= √4 + 4
= √16
= 4 units
∴ ABCD is a quadrilateral whose sides are equal but diagonals are not equal. Thus ABCD is a rhombus.
Hope it helps!